# Are there any uninformative priors with an unlimited support like $(-\infty,\infty), (0,\infty), (-\infty,0)$? [duplicate]

The Bayes theorem is:

$$P(\theta | x)=\displaystyle \frac{p(\theta)L_x(\theta)}{\int_{\theta \in A}p(\theta)L_x(\theta)d\theta}$$

It's pretty clear that $$\theta's$$ support will not change as bayes theorem update its distribution given some data, if $$\theta's$$ support is $$(a,b)$$ so it's easy to define a uninformative prior ( I'd just use $$U(a,b)$$) but when the support is either:

• $$A=(-\infty,\infty)$$
• $$A=(0,\infty)$$
• $$A=(-\infty,0)$$

it becomes trouble to get a non-informative prior like $$U(a,b)$$ so Is there any alternative for a uninformative prior distribution to get through this?

• Why do you need an uninformative prior? Such a thing doesn’t really exist.. If you really need, why not just using an improper “flat” prior?
– Tim
Commented Oct 14, 2021 at 22:23
• There is almost no prior information where I work.I've never been told about what flat prior is. Commented Oct 14, 2021 at 22:46